# Algebra 1A: Standard 8:

```Algebra 1P: Standard 3:
Name __________________________
Solving Absolute Value Equations Homework Worksheet # 1
Things to know: I know…


The absolute value of a number means its distance from zero.
To find the distance between 2 numbers, x and b, I calculate the absolute value of their difference: the
distance from x to b or from b to x = | x – b | = | b – x |.
 If the | x – b | = c, then x is c units from b in either direction.
Draw graphs for the following equations:
1. | x | = 3
-6 -4
-2
0
2
4
6
x = _____ or x = ______
4. | x – 1 | = 3
-6 -4
-2
3. | x – 0 | = 5
2. | x | = 2
0
-6 -4
-2
0
2
4
6
x = _____ or x = ______
5. | x – 4 | = 2
2
4
6
x = _____ or x = ______
7. | x + 2 | = 3
x = _____ or x = ______
10. | x – 4 | = 1
x = _____ or x = ______
-6 -4
-2
0
-6 -4
-2
0
2
4
6
x = _____ or x = ______
6. | x + 1 | = 5
2
4
6
x = _____ or x = ______
8. | x – 5 | = 0
x = _____ or x = ______
11. | x + 4 | = 2
x = _____ or x = ______
-6 -4
-2
0
2
4
6
x = _____ or x = ______
9. | x + 3 | = 4
x = _____ or x = ______
12. | x + 1 | = -5
x = _____ or x = ______
13. Graph the solutions for x if |x – b| = c. Which value is plotted first? _______ Which value tells the
distance? __________ Label the solution points in terms of b and c.
x
b
What can x equal? x = ___________ or x = ____________
Algebra 1P: Standard 3:
Name __________________________
Solving Absolute Value Equations Homework: Worksheet # 2
Things to know: I know…
 The absolute value of a number means its distance from zero.
 To find the distance between 2 numbers, x and b, I calculate the absolute value of
their difference: the distance from x to b or from b to x = | x – b | = | b – x |.
EX:
 If the | x – b | &lt; 6, then x is less than 6 units from b in either direction.
 If the | x – b | &gt; 6 number, then x is greater than 6 units from b in either direction.
Draw graphs for the following inequalities; then write the algebraic solutions:
1. | x | &gt; 2
x &lt; _____ or x &gt; ______
4. | x – 1 | &lt; 3
_____ &lt; x &lt; ______
____________________
6. | x + 1 | &lt; 4
x &lt; _____ or x &gt; ______
_____ &lt; x &lt; ______
8. | x – 5 | &lt; 0
____________________
10. | x – 4 | &lt; -1
x &lt; _____ or x &gt; ______
5. | x – 4 | &gt; 2
_____ &lt; x &lt; ______
7. | x + 2 | &gt; 3
3. | x – 0 | &gt; 4
2. | x | &lt; 5
9. | x + 3 | &gt; 0
____________________
____________________
11. | x + 4 | &gt; 2
____________________
12. | x + 1 | &lt; 5
___________________
13. Graph the solutions for x if |x – b| &lt; c.
Which value (b or c) is plotted first? ____________Which value tells the distance? ___________
Are the possible x values in one continuous region or two separate pieces of the graph? ____________
What can x equal? _______________________
x
14.
Graph the solutions for x if |x – b| &gt; c. Is the set of possible x values one
continuous region or two separate pieces of the graph? ____________
x
What can x equal? _______________________
Algebra 1P: Standard 3:
Name __________________________
Solving Absolute Value Equations Homework: Worksheet # 3
Example: | 5 – 2x | &lt; 3
2x
-6 -4
-2
0
x
0
2
1
5
5/2
8
4
Graph 2x: all points 3 or less units away from 5; 5-3 = 2 and 5+3 =8
Solution for 2x: All points between and including 2 and 8.
Graph x: divide the solution for 2x by 2: 2/2 = 1 and 8/2 = 4.
Solution for x: All points between 1 and 4, inclusive.
| 5 – 2x | &lt; 3  5 – 3 &lt; 2x &lt; 5 + 3
2 &lt; 2x &lt; 8
1&lt; x &lt;4
Solve the following absolute value inequalities first for ax and then for x. Draw the graph and write the
algebraic solution statement for each of the following problems:
1. | 3x | &gt; 2
2. | 2x | &lt; 5
3. | 4x – 0 | &gt; 8
3x
4x
2x
x
x
x
3x &lt; _____ or 3x &gt; ______
_____ &lt; 2x &lt; ______
4x &lt; _____ or 4x &gt; _____
x &lt; _____ or x &gt; ______
_____ &lt; x &lt; ______
x &lt; _____ or x &gt; ______
4. | 2x – 1 | &gt; 3
5. | 5x – 4 | &lt; 2
6. | 4 – 3x | &lt; 4
2x
5x
3x
x
x
x
2x &lt; _____ or 2x &gt; ______
_____ &lt; 5x &lt; ______
_____ &lt; 3x &lt; _____
x &lt; _____ or x &gt; ______
_____ &lt; x &lt; ______
_____ &lt; x &lt; _____
8. | 7 – 5x | &lt; 3
7. | 6x + 2 | &gt; 4
6x
x
9. | 2x + 3 | &gt; 5
5x
2x
x
x
6x: __________________
5x: __________________
2x: __________________
x: _________________
x: __________________
x: ___________________
```